with full diffraction-limited sampling of a scene. A guided-wave metamaterial aperture is used

to perform compressive image reconstruction at 10 frames per second of two-dimensional (range

and angle) sparse still and video scenes at K-band (18 to 26 gigahertz) frequencies, using

frequency diversity to avoid mechanical scanning. Image acquisition is accomplished with a 40:1

compression ratio.

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Downloaded from www.sciencemag.org on January 22, 2014 Metamaterial Apertures for Computational Imaging John Hunt et al. Science 339, 310 (2013); DOI: 10.1126/science.1230054 This copy is for your personal, non-commercial use only. If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here. Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here. The following resources related to this article are available online at www.sciencemag.org (this information is current as of January 22, 2014 ): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/339/6117/310.full.html Supporting Online Material can be found at: http://www.sciencemag.org/content/suppl/2013/01/16/339.6117.310.DC1.html http://www.sciencemag.org/content/suppl/2013/01/17/339.6117.310.DC2.html A list of selected additional articles on the Science Web sites related to this article can be found at: http://www.sciencemag.org/content/339/6117/310.full.html#related This article cites 26 articles, 2 of which can be accessed free: http://www.sciencemag.org/content/339/6117/310.full.html#ref-list-1 This article appears in the following subject collections: Physics http://www.sciencemag.org/cgi/collection/physics Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright 2013 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS. REPORTS surprising ease with which cyclopropanation activity could be installed into P450BM3 suggest that this approach will be useful for other synthetically important transformations for which biological counterparts do not yet exist. References and Notes 1. J. T. Groves, Proc. Natl. Acad. Sci. U.S.A. 100, 3569 (2003). 2. R. Breslow, J. Biol. Chem. 284, 1337 (2009). 3. T. K. Hyster, L. Knörr, T. R. Ward, T. Rovis, Science 338, 500 (2012). 4. J. B. Siegel et al., Science 329, 309 (2010). 5. H. M. L. Davies, J. R. Manning, Nature 451, 417 (2008). 6. H. Lebel, J.-F. Marcoux, C. Molinaro, A. B. Charette, Chem. Rev. 103, 977 (2003). 7. L. A. Wessjohann, W. Brandt, T. Thiemann, Chem. Rev. 103, 1625 (2003). 8. E. M. Isin, F. P. Guengerich, Biochim. Biophys. Acta Gen. Subj. 1770, 314 (2007). 9. J. R. Wolf, C. G. Hamaker, J.-P. Djukic, T. Kodadek, L. K. Woo, J. Am. Chem. Soc. 117, 9194 (1995). 10. B. Morandi, E. M. Carreira, Science 335, 1471 (2012). 11. C. J. C. Whitehouse, S. G. Bell, L.-L. Wong, Chem. Soc. Rev. 41, 1218 (2012). 12. J. C. Lewis, F. H. Arnold, Chimia (Aarau) 63, 309 (2009). 13. Materials and methods are available as supplementary materials on Science Online. 14. A. Caballero, A. Prieto, M. M. Diaz-Requejo, P. J. Perez, Eur. J. Inorg. Chem. 2009, 1137 (2009). 15. I. Nicolas, P. Le Maux, G. Simonneaux, Coord. Chem. Rev. 252, 727 (2008). 16. U. T. Bornscheuer, R. J. Kazlauskas, Angew. Chem. Int. Ed. 43, 6032 (2004). 17. O. Khersonsky, C. Roodveldt, D. S. Tawfik, Curr. Opin. Chem. Biol. 10, 498 (2006). Acknowledgments: This work was funded by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through grant DE-FG02-06ER15762. E.M.B. was supported by a Ruth M. Kirschstein National Institutes of Health (NIH) postdoctoral fellowship, award number F32GM087102, from the National Institute of General Medical Sciences and a generous startup fund from the University of North Carolina Chapel Hill. P.S.C., E.M.B., and F.H.A. have filed through the California Institute of Technology a provisional patent application that is based on the results presented here. The authors thank Z. J. Wang for helpful discussions during the preparation of the manuscript. Supplementary Materials www.sciencemag.org/cgi/content/full/science.1231434/DC1 Materials and Methods Supplementary Text Figs. S1 to S3 Tables S1 to S20 References (18–35) 12 October 2012; accepted 30 November 2012 Published online 20 December 2012; 10.1126/science.1231434 Metamaterial Apertures for Computational Imaging John Hunt,1,4* Tom Driscoll,1,2,4 Alex Mrozack,3 Guy Lipworth,1,4 Matthew Reynolds,4 David Brady,4 David R. Smith1,4 By leveraging metamaterials and compressive imaging, a low-profile aperture capable of microwave imaging without lenses, moving parts, or phase shifters is demonstrated. This designer aperture allows image compression to be performed on the physical hardware layer rather than in the postprocessing stage, thus averting the detector, storage, and transmission costs associated with full diffraction-limited sampling of a scene. A guided-wave metamaterial aperture is used to perform compressive image reconstruction at 10 frames per second of two-dimensional (range and angle) sparse still and video scenes at K-band (18 to 26 gigahertz) frequencies, using frequency diversity to avoid mechanical scanning. Image acquisition is accomplished with a 40:1 compression ratio. Imaging systems can be characterized by object dimension [for instance, two-dimensional (2D) for photographs] and information dimension (for example, the number of pixels in an image). Conventional imaging systems are built around the assumption that the object dimension must be conserved in the information dimension, regardless of the inherent information content of the scene. Compressive measurement leverages the realization that measurements need not conserve form of dimension in this sense (1–3). Indeed, the concept of dimension indicates that measurements are well ordered in some space, implying that adjacent measurements sample similar object data. Information-transfer efficiency, however, is maximized if object data measured 1Center for Metamaterials and Integrated Plasmonics, Duke University, Box 90291, Durham, NC 27708, USA. 2Department of Physics, University of California San Diego, La Jolla, CA 92093, USA. 3Fitzpatrick Institute for Photonics and Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA. 4Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA. *To whom correspondence should be addressed. E-mail: john.hunt@duke.edu by successive measurements are as distinct as possible. At the diffraction limit, the finite size of the aperture used to form an image imposes a maximum pixel dimension N equal to the spacebandwidth product (SBP), which represents the number of measurement modes needed to exactly reproduce an arbitrary scene (4, 5). In a conventional imaging system, the measurement modes might be thought of as diffraction-limited spots, each of which samples a small portion of the scene (Fig. 1A). Because these modes have little or no spatial overlap in the detector plane, they can be acquired nearly independently and simultaneously with N detectors, such as a chargecoupled device array. However, for natural scenes, many of the modes provide little to no useful data; therefore, they can be substantially compressed without excessive loss of image fidelity (6). The concept of a measurement mode can be generalized, such that the imaging process can be expressed mathematically by the relation g = Hf, where g is a collection of measurements, H is the measurement matrix (a row-wise array of all measurement modes), and f is the sampled scene. To form a completely determined data set of measurements (thus enabling a unique linear solution for f), the rank of H must equal the scene’s data dimension (7). Compressive sampling allows reconstruction of underdetermined scenes, finding f by solving the minimization problem arg minf ‖g − Hf ‖22 þ lRðfÞ, where arg minf denotes the value of f that minimizes the expression, l is a scalar weighting factor, and R(f ) expresses some prior knowledge about the likely composition of the scene. Typically in compressive sampling, R is the l1-norm of the scene, represented in an appropriate basis, which reflects the inherent sparsity that exists in natural scenes. This nonlinear minimization problem is rigorously solvable, even with highly underdetermined measurement data sets (8–10). Imaging systems for radio frequency and millimeter-wave electromagnetics have generally been of two types: scanned single-pixel systems and multielement phased-arrays (or synthetic phased arrays). The measurement modes used by classical single-pixel systems are typically inefficient at collecting imaging data. For instance, a rasterizing scanned beam collects information about only one point in space at a time. Multielement phased array systems have much more flexibility in the measurement modes they can access, but these systems sacrifice the size, weight, power, and price advantages of single-pixel systems. New approaches to imaging at these frequencies have made use of lenses and spatially modulated masks combined with single-pixel detectors to make compressed measurements. One of the pioneering implementations of this form of compressive imaging, depicted in Fig. 1B, was carried out at optical (11) and terahertz frequencies with the use of random static (12) and dynamic (13) masks. Other groups have presented additional ways to introduce mode diversity (14). We show that metamaterial apertures have distinct advantages for compressive imaging because they can be engineered to support custom-designed complex measurement modes that vary with frequency. Leveraging the same electromagnetic 310 18 JANUARY 2013 VOL 339 SCIENCE www.sciencemag.org REPORTS Fig. 1. Comparison of (A) conventional and (B and C) compressive imaging schemes. A conventional imager uses a lens to form measurement modes that effectively map all parts of an object to a detector/image plane. Each mode contributes highly specific and localized information, and all modes can be captured simultaneously with a pixel array or other detector. Within singlepixel schemes, many types of modes can be used to form the image, with measurements being captured sequentially. In the example shown in (B), a random mask and two lenses are used to project incoherent modes that sample the entire scene. The microwave metamaterial imager reported here (C) makes use of a planar waveguide that feeds a holographic array of ELCs, removing the need for lenses. The waveguide acts as a coherent single-pixel device, with the array of ELCs serving to produce the illuminating complex spatial modes. flexibility that metamaterials have shown in many other contexts (15–20), we can construct an imaging aperture suitable for single-pixel operation that can project nearly arbitrary measurement modes into the far-field, constrained only by the size of the aperture and resonant elements. We use a 1D metamaterial aperture to perform compressed imaging of various 2D (one angle plus range) canonically sparse scenes. Our imaging device consists of a leaky waveguide, Fig. 2. Simulated far-field profiles for the metamaterial aperture at two frequencies: 18.5 GHz (A) and 21.8 GHz (B). Resonant metamaterial apertures (C) can create mode distributions that vary with frequency. (D) Measured magnitude of the measurement matrix, H, as a function of angle and frequency. formed by patterning the top conductor of a standard microstrip line with complementary electric-inductor-capacitors (cELCs) (21, 22) metamaterial elements (Fig. 2C). This configuration is equivalent to the schematic of the compressive imager in Fig. 1C, except that the aperture becomes one-dimensional. Each cELC acts as a resonant element that couples energy from the waveguide mode to free space. The resonance frequency and spectral shape of each cELC controls the amplitude and phase of the transmitted wave, such that the far-field modes can be designed by modifying the geometry of the cELCs along the microstrip. By controlling the design and distribution of the individual elements, which affect both the scattered-field characteristics as well as the guided-wave characteristics, nearly any desired aperture mode can be created. For canonically sparse scenes, an efficient set of measurement modes are those that distribute energy randomly across both the amplitude and phase space of the scene. The dispersion present in resonant metamaterial elements makes frequency a natural choice for indexing the modes, creating a mapping between the measurement modes and frequency. Thus, by sweeping the frequency of the illuminating signal across the available bandwidth, we access the aperture modes sequentially, without having to move or reconfigure the aperture. For image reconstruction schemes that use an arbitrary set of measurement modes, it is essential that the modes be as orthogonal as possible to each other, which places demands on the sharpness and separation of the resonances, with sharper resonances yielding less correlated modes. We have fabricated a random-mode metamaterial aperture, 40 cm in length, designed to operate in the K band from 18.5 to 25 GHz. Two samples of the measurement modes for this design are plotted in Fig. 2, A and B, and the complete measurement matrix is plotted in Fig. 2C. In our demonstration, scenes are illuminated by far-field radiation from a single source: a lowdirectivity horn antenna. Backscattered radiation from objects in the scene floods the metamaterial www.sciencemag.org SCIENCE VOL 339 18 JANUARY 2013 311 REPORTS Fig. 3. (A) Reconstructions of four different static scenes (differentiated by color), consisting of two (black, green, and blue) or three (red) 10-cm scattering objects. The solid “+” symbols show the actual location of objects, and the pixels show the reconstructed image. Pixel size reflects the maximum instrument resolution. The image has been cropped from the full field of view of T70°. (B) Photograph of a single scene corresponding to the black markers in (A). Fig. 4. (Left) Image of a single moving object at 10-Hz frequency. Each voxel is sized to match the spatio-temporal resolution of the metamaterial aperture, and the amplitude of the reconstructed scattering density is mapped to the transparency of each voxel. Voxels are also colorcoded in time, from blue to red. (Right) Data projections in two dimensions. aperture, which selectively admits only one specific mode at each measured frequency. The resulting (complex) signal is measured by a vector network analyzer. We formed several simple sparse scenes inside an anechoic chamber with dimensions of 4 m by 4 m by 3 m. Each scene contained two or three scattering objects (retroreflectors), 10 cm in diameter, located at arbitrary positions in the chamber. Figure 3B shows one such scene. All scenes were reconstructed using the TwIST code (23). For an aperture of this size and bandwidth, the diffraction-limited angular resolution is 1.7°, and the bandwidth-limited range resolution is 4.6 cm. Across a field of view of T70° in angle and 1.5 to 4 m in range, the equivalent SBP = 4475. Our measurement, however, contains only 101 values, representing a compression ratio of more than 40:1. We note that the acquisition of a complete data set for the scenes in Fig. 3 requires only 100 ms, which makes the imaging of moving scenes a tantalizing possibility. To demonstrate the imaging of moving scenes, we performed repeated 100-ms sweeps while moving an object through the scene. The acquisition speed in this experiment was limited by the signal-to-noise-ratio—primarily due to the network analyzer, which is designed for operational flexibility rather than high dynamic range or sweep speed. We imaged a single scattering object moving through the scene on a linear path at ~0.2 m/s. Figure 4 depicts the reconstructed scene. The object position in angle and range, mapped as a function of time, is observed in the retrieved scene. These data are presented in video format along with a camera recording of the object motion in movie S1. A major advantage of metamaterial radiators in this application is the ability to incorporate tuning (24–27). Dynamically varying the resonance of the metamaterial elements would enable reconfigurable measurement modes. Dynamic tuning also frees the frequency bandwidth, effectively enabling hyperspectral imaging (28). The imaging system we present here combines a computational imaging approach with custom aperture hardware that allows compression to be performed on the physical layer that is used to do the illumination and/or recording. The use of metamaterials is a convenient tool for the creation of such apertures, as metamaterial techniques offer a well-understood design path. Leveraging the resonant nature of metamaterial elements also creates frequency diversity of the measurement modes, giving an all-electrical method of quickly sweeping through a mode set. This metamaterial approach scales linearly with frequency through terahertz frequencies with correspondingly higher resolutions. Due to their small form factor and lack of moving parts, similar systems may extend microwave and millimeterwave imaging capabilities. References and Notes 1. E. J. Candès, Proc. Int. Congress Math. 3, 1433 (2006). 2. D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006). 312 18 JANUARY 2013 VOL 339 SCIENCE www.sciencemag.org 3. C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, D. J. Brady, Appl. Opt. 49, E67 (2010). 4. E. Abbe, J. R. Microsc. Soc. 3, 790 (1883). 5. A. W. Lohmann, in “The space–bandwidth product, applied to spatial filtering and holography,” Research Paper RJ-438 (IBM San Jose Research Laboratory, San Jose, CA, 1967), pp. 1–23. 6. R. M. Willett, R. F. Marcia, J. M. Nichols, Opt. Eng. 50, 072601 (2011). 7. D. J. Brady, Optical Imaging and Spectroscopy (Wiley, Hoboken, NJ, 2008). 8. E. J. Candès, C. R. Math. 346, 589 (2008). 9. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, S. Lim, Opt. Express 17, 13040 (2009). 10. L. Potter, E. Ertin, J. Parker, M. Cetin, Proc. IEEE 98, 1006 (2010). 11. D. Takhar et al., Proc. SPIE Comput. Imaging IV 6065, 606509 (2006). 12. W. L. Chan et al., Appl. Phys. Lett. 93, 121105 (2008). REPORTS 13. W. L. Chan et al., Appl. Phys. Lett. 94, 213511 (2009). 14. A. Mahalanobis, M. Neifeld, V. K. Bhagavatula, T. Haberfelde, D. Brady, Appl. Opt. 48, 5212 (2009). 15. J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 (2006). 16. T. Driscoll et al., Appl. Phys. Lett. 88, 081101 (2006). 17. N. B. Kundtz, D. R. Smith, Nat. Mater. 9, 129 (2010). 18. Y. Urzhumov, D. R. Smith, Phys. Rev. B 83, 205114 (2011). 19. E. Narimanov, Nat. Mater. 7, 273 (2008). 20. Z. Jacob, L. V. Alekseyev, E. Narimanov, Opt. Express 14, 8247 (2006). 21. R. Liu et al., Appl. Phys. Lett. 94, 073506 (2009). 22. J. D. Baena et al., IEEE Trans. Microw. Theory Tech. 53, 1451 (2005). 23. J. M. Bioucas-Dias, M. A. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007). 24. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006). 25. T. Driscoll et al., Science 325, 1518 (2009). 26. H. T. Chen et al., Nature 444, 597 (2006). 27. D. Shrekenhamer et al., Opt. Express 19, 9968 (2011). 28. Z. Xu, E. Y. Lam, J. Opt. Soc. Am. A Opt. Image Sci. Vis. 27, 1638 (2010). Acknowledgments: This work was supported by a grant from the Air Force Office of Scientific Research (no. FA9550-09-1-0539). Data and code are available at http://people.duke.edu/~jdh51/Data_Metamaterial_ Apertures_for_Computational_Imaging.zip. Supplementary Materials www.sciencemag.org/cgi/content/full/339/6117/310/DC1 Supplementary Text Figs. S1 to S3 Movie S1 11 September 2012; accepted 22 November 2012 10.1126/science.1230054 Climate Events Synchronize the Dynamics of a Resident Vertebrate Community in the High Arctic Brage B. Hansen,1†‡ Vidar Grøtan,1† Ronny Aanes,1,2* Bernt-Erik Sæther,1 Audun Stien,3 Eva Fuglei,2 Rolf A. Ims,4 Nigel G. Yoccoz,4 Åshild Ø. Pedersen2 Recently accumulated evidence has documented a climate impact on the demography and dynamics of single species, yet the impact at the community level is poorly understood. Here, we show that in Svalbard in the high Arctic, extreme weather events synchronize population fluctuations across an entire community of resident vertebrate herbivores and cause lagged correlations with the secondary consumer, the arctic fox. This synchronization is mainly driven by heavy rain on snow that encapsulates the vegetation in ice and blocks winter forage availability for herbivores. Thus, indirect and bottom-up climate forcing drives the population dynamics across all overwintering vertebrates. Icing is predicted to become more frequent in the circumpolar Arctic and may therefore strongly affect terrestrial ecosystem characteristics. In the Arctic, climate is now changing rapidly (1), affecting the population dynamics of many species, as well as trophic interactions among them (2). It is well recognized (3) that spatial correlations in climate can enforce synchronous fluctuations among populations within the same species [the “Moran effect” (4)]—increasing the likelihood of species extinctions (5, 6). More far-reaching consequences may be expected if such climateenforced synchronization acts on the level of 1Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway. 2Norwegian Polar Institute, Fram Centre, NO-9296 Tromsø, Norway. 3Norwegian Institute for Nature Research, Fram Centre, NO-9296 Tromsø, Norway. 4Department of Arctic and Marine Biology, University of Tromsø, NO9037 Tromsø, Norway. *Present address: Norwegian Directorate for Nature Management, Tungasletta 2, NO-7047 Trondheim, Norway. †These authors contributed equally to this work. ‡To whom correspondence should be addressed. E-mail: brage.b.hansen@ntnu.no ecological communities (7, 8). However, linking cross-species synchrony to common environmental drivers has proven difficult as variation among species in the form of density regulation and response to other environmental drivers often has a desynchronizing effect (9). Thus, observed synchrony usually results from trophic interactions, such as the cofluctuations among predators because of shared prey (3). Nonetheless, one rare example of vertebrates that fluctuate synchronously but are not linked by trophic interactions comes from the Arctic, where populations of caribou (Rangifer tarandus) and musk oxen (Ovibos moschatus) on opposite coasts of Greenland seem synchronized by large-scale weather oscillations (7), but see (10). Here, we ask how climate and weather events influence population dynamics across the entire overwintering vertebrate community on the higharctic island of Spitsbergen, Svalbard (Fig. 1 and fig. S1). In winter, this trophic system at 78°N includes only three herbivores, the wild Svalbard reindeer (R. t. platyrhynchus), Svalbard rock ptarmigan (Lagopus muta hyperborea), and sibling vole (Microtus levis), as well as their shared consumer, the arctic fox (Vulpes lagopus). The species are sympatric and widely distributed across the archipelago, except for the vole, which is only found in a small bird cliff area (11). In the short summer season, migratory birds including seabirds, geese, and waders also breed in Svalbard, and polar bears (Ursus maritimus) occasionally go on shore throughout the year. However, the few resident terrestrial vertebrates and the lack of widespread endemic arctic rodents with multiannual population cycles, such as arctic lemmings (Lemmus spp. and Dicrostonyx spp.), makes the Svalbard terrestrial food web and its trophic dynamics simpler than many other high-arctic ecosystems (12). We found correlated population fluctuations across all four overwintering members of the community (Fig. 1), specifically the presence of positive interspecific correlations in the annual changes in population sizes or population indexes (13) when the arctic fox data were advanced by 1 year (Figs. 2B and 3). One plausible hypothesis explaining this synchrony is that climate influences the herbivores in a broadly similar way because of common effects on plant availability, operating through variation in snowpack properties or vegetation growth. This generates bottom-up effects on their shared consumer. To test this, we fitted linear regressions (13) that modeled population growth rate as a function of log population size (or index) and weather covariates obtained from a local weather station that were expected to influence the herbivore food supply. Model selection (table S1) suggested that, after accounting for density dependence, the number of rainy days in winter (hereafter, “winter rain”) (Fig. 2A) was the best predictor of annual population growth rates across species. Winter rain had a significantly negative effect on all species (tables S2 to S5). Model selection also revealed an additional positive effect of summer temperature on the species’ www.sciencemag.org SCIENCE VOL 339 18 JANUARY 2013 313